I have been struggling with maths.

Now, what makes this incredibly difficult is that I DO know a bit about coding functions in a number of languages, which ALL have an IF statement of some sort. But, that ain't gonna work, here. I have to come up with a math-based solution which Poser will then form into a nodal thingie to perform the processing on colour I need.

And my knowledge of math functions is shocking. Or even, how to problem-solve in maths.

I mean, I look at simple maths such as x = (x + 1) / 2 (okay, it was f(x) = (x + 1) / 2 but for all intents and purposes, your function was defined in "= (x + 1) / 2", the averaging bit, and your purpose was, in your words, to "find a straightforward manipulation of the two colors such that I'd produce new colors that were not hidden colors, and were visibly different from each other. Thus you would see that you got two different results" which you did using a formula where basically did averaging. To come up with that sort of solution would mean to go back to remedial algebra word-problem solving.

For instance:
Solve for 1 or less than 1 but not less than 0.

This is what you are asking with:
"How would you detect a hyper color ( > 1) - a color with a component greater than 1? (Remember you cannot directly "see" hyper colors - 1 is the brightest your monitor will go.) There are many ways - I'll wait for any of you to figure one out. Show me with math, and with nodes."

Right?

Clueless.

I looked at MOD(x)... now, if I read this correctly, modulus turns any number into a real number, right? which is great, at least we can rule out negative numbers, but then I want to solve for 1. This is the key next step. Define where I am here, and I've laughin'.

I so did try. And came up with:

x = MOD(x - (x/1 x 1/x))

Rubbish. Not a solution at all! Might as well have said 1 instead of (x/1 x 1/x)). Like I'm trying to do a clamp or something.

Anyway.... lost but persevering on...

Monterey/Mint21.x/Win10 - Blender3.x - PP11.3(cm) - Musescore3.6.2

Wir sind gewohnt, daß die Menschen verhöhnen was sie nicht verstehen
[it is clear that humans have contempt for that which they do not understand] 

Metaphor of Chooks